Receiver for Verification using Entangled Photons

ABSTRACT

A method of generating a verification code includes measuring a time of arrival and a corresponding first or second state value of a plurality of first photons and a plurality of second photons, where respective ones of the plurality of first photons are entangled with respective ones of a plurality of second photons in a first basis, which is time, and entangled in a second basis. A first and a second ordered list of the measured times of arrival of the plurality of respective first and second photons is generated. Time-of-arrival matches between the first ordered list and the second ordered list are determined. First or second state values that correspond to the determined time-of-arrival matches between the first ordered list and the second ordered list are determined. A verification code using some of the determined first or second state values that correspond to the determined time-of-arrival matches is generated.

CROSS REFERENCE TO RELATED APPLICATION

The present application is a non-provisional of U.S. ProvisionalApplication Ser. No. 63/356,534, filed on Jul. 29, 2022. The presentapplication is also a continuation-in-part of U.S. patent applicationSer. No. 17/465,235, entitled “Method for Synchronizing and LockingClocks”, filed on Sep. 2, 2021, which is a non-provisional applicationof U.S. Provisional Patent Application No. 63/118,542, entitled “Systemand Method for Sharing Quantum Entanglement”, filed on Nov. 25, 2020, isa non-provisional application of U.S. Provisional Patent Application No.63/186,754, entitled “System and Method for Sharing QuantumEntanglement”, filed on May 10, 2021, and is a non-provisionalapplication of U.S. Provisional Patent Application No. 63/218,433,entitled “System and Method for Sharing Quantum Entanglement”, filed onJul. 5, 2021. The entire contents of U.S. patent application Ser. No.17/465,235, and U.S. Provisional Patent Application Nos. 63/356,534,63/118,542, 63/186,754, and 63/218,433 are herein incorporated byreference.

INTRODUCTION

Entanglement is a valuable quantum resource that allows information tobe shared between different users with properties that are not possiblewith classical sharing schemes. Methods and systems that support andimprove the distribution and use of entangled quantum resources forvarious applications are and will be useful in advancing art.

BRIEF DESCRIPTION OF THE DRAWINGS

The present teaching, in accordance with preferred and exemplaryembodiments, together with further advantages thereof, is moreparticularly described in the following detailed description, taken inconjunction with the accompanying drawings. The skilled person in theart will understand that the drawings, described below, are forillustration purposes only. The drawings are not necessarily to scale;emphasis instead generally being placed upon illustrating principles ofthe teaching. The drawings are not intended to limit the scope of theApplicant's teaching in any way.

FIG. 1 illustrates an embodiment of an authentication and verificationsystem and method using entangled photons of the present teaching.

FIG. 2A illustrates an embodiment of a time-based state comb for anauthentication and verification system and method using entanglement ofthe present teaching.

FIG. 2B illustrates an embodiment of a time-based state comb for anauthentication and verification system and method using entanglementbeing correlated of the present teaching.

FIG. 3 illustrates an embodiment of a system for generating a sharedmeasurement comb in time and polarization for an entangled photonauthentication and verification system of the present teaching.

FIG. 4 illustrates generated combs for an embodiment of anauthentication and verification application using entangled photons ofthe present teaching.

FIG. 5 illustrates embodiments of generated state combs with noise in anembodiment of an authentication and verification application usingentangled photons of the present teaching.

FIG. 6A illustrates state combs with timestamps for an embodiment of asystem and method of authentication and verification using entanglementof the present teaching.

FIG. 6B illustrates the embodiment of state combs for the system andmethod of authentication and verification using entanglement with noiseof the present teaching.

FIG. 6C illustrates an embodiment of correlating state combs of FIG. 6B.

FIG. 7 illustrates an embodiment of an authentication and verificationsystem and method using entangled photons with a trusted authority ofthe present teaching.

DESCRIPTION OF VARIOUS EMBODIMENTS

The present teaching will now be described in more detail with referenceto exemplary embodiments thereof as shown in the accompanying drawings.While the present teachings are described in conjunction with variousembodiments and examples, it is not intended that the present teachingsbe limited to such embodiments. On the contrary, the present teachingsencompass various alternatives, modifications and equivalents, as willbe appreciated by those of skill in the art. Those of ordinary skill inthe art having access to the teaching herein will recognize additionalimplementations, modifications, and embodiments, as well as other fieldsof use, which are within the scope of the present disclosure asdescribed herein.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin connection with the embodiment is included in at least one embodimentof the teaching. The appearances of the phrase “in one embodiment” invarious places in the specification are not necessarily all referring tothe same embodiment.

It should be understood that the individual steps of the methods of thepresent teachings can be performed in any order and/or simultaneously aslong as the teaching remains operable. Furthermore, it should beunderstood that the apparatus and methods of the present teachings caninclude any number or all of the described embodiments as long as theteaching remains operable.

Entanglement is a resource that can be used in a variety of quantumand/or classical systems. Entanglement refers to a quantum system thatshares quantum state information such that measurements of the system,even if performed at different times and/or places yields measuredquantum states that are perfectly correlated.

One feature of the present teaching is that it supports the use ofso-called “high brightness” single-photon sources to generate quantumentangled photon pairs that are shared. Some of these high-brightnesssources create large numbers of quantum entangled pairs usingSpontaneous Parametric Down Conversion (SPDC). These systems areoptically pumped crystals with a laser source. The crystals emit photonsthat are entangled in one or more basis which may include polarization,frequency (color), space, and/or time. Photons that are entangled inmore than one basis can be referred to as carrying a hyperentangledstate. In this case, two or more different measured state values arecorrelated across the pair of entangled photons. Thus, the state of thephoton emitted in this multi-dimensional quantum state can be measuredand represented as having a time, a position, a frequency and/or apolarization. In various embodiments, numerous subsets of the possiblestates are generated, measured, formulated as a comb and/or shared as acomb. This can be a time-bin comb representation and/or a timestamp combrepresentation.

A comb is a list of values of selected measured states. Said anotherway, a comb is an ordered list of measurement events. In someembodiments, a comb is a list of measured states in the order theyarrive at a measurement node and/or at a particular detector or group ofdetectors in the measurement node. In some embodiments, a comb is a listof measured states in an order they are measured. In some embodiments acomb is a list of measured states and/or the time of arrival. In someembodiments, a comb is an ordered list of measured events from differentspatial positions. In other embodiments, a comb is an ordered list ofmeasured events from different polarizations. In other embodiments, acomb is an ordered list of measured events from different colors. In yetother embodiments, a comb is a combination of measured events that mayinclude any combination of the above and any other type measured events.

The comb time can be measured from various reference points in variousembodiments. In some embodiments, the come time is measured using alocal clock. In some embodiments, the local clock is synchronized in arelative and/or absolute basis to a non-local clock using systems andmethods known by those skilled in the art. In some embodiments, theclocks are free running clocks that are synchronized using sharedentanglement. In some embodiments, a comb includes more than one valueper measured state. The value can be, for example, polarization, arrivaltime, frequency/color and/or spatial position. This is the case, forexample, if an entangled state is a hyper-entangled state, where asingle photon of a pair or set is entangled in more than one way(dimension or basis). In some embodiments, different members of a combhave different values. That is, a comb can include more than one type ofentangled state where the more than one types are not entangled witheach other. This could be the case, for example, if quantum states fromtwo different sources generating entangled states were multiplexed. Thiscould be done, for example, to increase the rate of entangled pairsbeing generated.

In SPDC sources, the time entanglement occurs as photons created by thisprocess are “born” at the same moment in time with absolute precision(Δt=0), although the actual birth time is a random process and unknownand thus satisfies the superposition requirement for being quantumentangled.

The frequency, which can also be referred to in the art as color orwavelength, entanglement occurs due to the conservation of energy. Forphotons, E=hv where his Planck's constant and v is the frequency. Theenergy in the laser pump photons (frequency/color) determines whatfrequencies are available to the entangled photons that are generated bythe process. However, any given pair of generated photons can be in anyallowed combination and thus the particular color is unknown at thesource, satisfying the conditions for being quantum entangled. As oneexample, for frequency entanglement, if VL is the frequency of the pumpand Vi is the frequency of the idler photon, and Vs is the frequency ofthe signal photon, then: E=hVL=hVi+hVs, or E/h=VL=Vi+Vs.

Polarization entanglement can be realized by using two crystalsback-to-back with a length that is less than a coherence length of thepump source. Each crystal is configured to generate a particularpolarization state of the output based on an input polarization of thepump. However, it is unknown at the output of the back-to-back crystalswhich crystal generated the pair, and thus what polarization state of agiven pair is unknown at the source, satisfying the conditions for pairsbeing quantum entangled in polarization.

Spatial entanglement is realized by relying on conservation of momentum.In general, there can be multiple spatial directions along which pairsare provided that is based on the birefringent properties of thecrystal. In these configurations, a particular one of two, or one of acontinuous spatial region (e.g. a cone-shaped region) of a position of aparticular pair is unknown at exit to the crystal. This then satisfiesthe conditions for pairs being quantum entangled in space. The spatialentanglement could be, for example, one of two positions, but it couldalso be entangled in more dimensions and up to a continuous set ofdimensions.

A feature of the temporal and spatial bases, therefore, is that theamount of information of a particular measurement can be substantiallyhigher than the amount of information in a basis of entanglement that isa “one of two” possibilities basis. Generally, depending on a particularbasis type of the entanglement, the measurement can represent an outcomethat is one of two, sometimes referred to as a qubit configuration, oneof three, one of four, etc. up to a full continuum of values. It shouldbe understood that the information within a continuum of values is onlylimited by the resolution of the measurement apparatus. We refer hereinto the extent or number of possible measurement outcomes of a particularbasis as the “state dimension” of the basis. It should be understoodthat the term “state dimension” is different from the term “dimension”,which is also used herein as applied to entanglement. In the art theterm “dimension” is sometimes another word for the term “basis”. Theusage is clear from the context of the discussion of the presentteaching. One skilled in the art will appreciate that the quantumliterature uses these various terms interchangeably.

Continuous values as part of an entanglement measurement are practicallylimited by the measurement resolution available for measuring thatbasis' dimensions. Entanglement basis types that provide a continuousset of values (continuous state dimension) are sometimes referred to asa continuous variable configuration. As described herein, both countableand continuous entangled dimensions are amenable to using the system andmethod of measurement comb sharing of the present teaching. Each type ofbasis provides various and sometimes different benefits, e.g. noiseand/or background immunity, within a particular embodiment of a systemand method of entanglement sharing that uses state combs of the presentteaching.

One feature of the present teaching is that systems and methods ofauthentication and verification using entanglement can rely on entangledphotons that are hyperentangled in time and polarization. We note thatin the art, the terms “authentication” and “verification” are sometimesused interchangeably. For purposes of this disclosure, the term“verification” generally refers to a process that verifies an identityand/or an accuracy of data and/or the source of the data. The term“authentication” generally refers to the identification of and accuracy(e.g. trustworthiness) of a user and/or a role of a user connected tothe generation of data. The data can include, for example, credit cardnumbers, prices, product codes, transaction data, and/or sensor data.Users can include individuals, but also may refer to a data generatingdevice, for example, a robot, sensor or a terminal, which can have arole and/or identity as part of a system.

FIG. 1 illustrates an embodiment of an authentication and verificationsystem 100 and method using entangled photons of the present teaching.An entangled source 102 generates pairs of entangled photons. One of thepair is sent to a device 104. The device 104 can be a handheld device,for example, a cell phone or other personal device. The other of thepair is sent to another device 106. The other device 106 can be, forexample, an authentication terminal, a point-of-sale terminal, a systemserver, or numerous other processing devices. The device 104 and thedevice 106 are connected via a classical communication channel 108. Theentangled source 102 delivers entangled photons to a device 104 and theother device 106. The device 104 can be, as just some examples, a cellphone, tablet, watch, card, personal locator, sensor and/or specializedprocessor. The other device 106 can be, as just some examples, a pointof sale terminal, a computer, a laptop and/or any of a number of fixedor handheld processing devices.

The devices 104, 106 can be connected to users that need authenticationand verification services that connect, stamp, notate, mark, orotherwise associate information transfer(s) between the two devices 104,106. In one embodiment of the authentication and verification system 100the device 104 is a handheld device and the other device 106 is anauthentication terminal. But this is just one example. For example, andas understood by those skilled in the art, either of handheld deviceand/or the authentication terminal can be any of numerous elements thatform two sides of an authentication or verification system. That couldinclude, numerous fixed or mobile assets, for example, sensor devices,robots, various pieces of equipment, and/or various computing andprocessing systems.

The device 104 and the other device 106 measure the photons generated bythe source 102 in at least two bases. In some embodiments, the bases canbe polarization and time. In some embodiments, the bases can be positionand time. In some embodiments, the bases can be position andpolarization. A measurement comb that includes measurements of one ofthe bases is exchanged over the classical channel 108. Most of theexamples presented herein use a comb that is a time-based comb, but ingeneral a comb is an ordered list of measurement events and is notnecessarily time-based. So, for example, a position and polarizationmeasurement comb can be a list ordered by specific positions and thevalue of polarization associated with that position. Positionmeasurement alone can be an ordered list based on the order of position.Position measurement alone can also be an ordered list based on themeasured position value in a time order based on when the position ismeasured. What is characteristic of the operation of the method andsystem of the present teaching is that combs generated in two separatemeasurements, one for each of the pair of entangled photons, andassociated background measurements are prepared with the same orderingscheme to support the efficient matching and pair identification usingthe two combs.

The classical channel 108 in some embodiments is a Bluetooth™ channel.Both the device 104 and other device 106 determine a match in themeasurement comb. This can be achieved using for example, bycross-correlation or a process of offset and matching of the basisinformation that has been exchanged. The match information is used byboth the device 104 and the other device 106 to determine which measuredphoton events are entangled. Those photons values, measured in the otherbasis become a shared secret held between the device 104 and the otherdevice 106. That shared secret can be used as a one-time pad,cryptographic key, and/or a transaction identification number.

In some embodiments, the entangled source 102 generates photons at anoutput such that the device 104 needs to be placed by the consumer in aspecific location. For example, the entangled source 102, might generateentangled photons that illuminate a small region in space, and theanalyzer and/or detectors in the device 104 must be within theilluminated area. In some embodiments, the entangled source 102generates photons that are spread over a larger area, and the device 104can be placed within the larger area. In some embodiments, the entangledsource 102 generates photons that are coupled into one end of an opticalfiber and the device 104 is configured to plug into the other end of theoptical fiber.

In some embodiments, the entangled source 102 generates photons that areentangled in more than two bases. The third basis is also measured bythe devices 104, 106 and associated with the time of arrival. In someembodiments, the measurements of the values of the third basis are usedto generate more bits of random number that can be used as averification code. For example, a two-dimensional basis will yield onebit per measurement (a zero or a one, for H or V). An extra basis canadd the additional dimension of that basis for each entangled pair. Forexample, three colors and two polarization provide five bits, so thevalues are coded as one of one through five values for each number. Thethird basis measurements can also be used as an error check. If a valueof the one basis is measured to produce a random number value, but avalue of the third basis is not available at that time of arrival, thenan error condition can be raised.

The verification code can be used in numerous ways. For example, theverification code can be attached to a purchase by both the owner of theother device 106 and the owner of the device 104, as a unique identifierof the purchase. The verification code can be used as a crypto key forsecurely transmitting a credit card number of the user of the device104, that can be decoded only by the owner of the device 106 to securethe card for only the particular transaction. Two verification codes canbe used for both purposes on a single transaction. The verification codecan be attached to transaction data associated with transaction betweenthe devices 104, 106, thereby verifying the transaction. Theverification code can be used by a sensor (e.g. device 104) when sendingsensor data to a server (e.g. device 104) to uniquely identify thereceived data as being from a particular sensor. The verification codegenerated in one device 104 can be XORed with data in that device 104 togenerate secret data (scrambled) and then the secret data subsequentlyXORed with a verification code generated in the other device 106 toregenerate the data (unscramble) if the two verification codes arederived from entangled pairs.

The verification code can also be used to authenticate a user of adevice 104 or the device 104 itself. In some embodiments, theverification code is sent to a trusted authority that holds theverification code in a repository (not shown). In a subsequenttransaction with device 104 that can be with the device 106 or with acompletely different device (not shown), the transacting device 106 canquery the repository, for example, but having the device 104 resend theverification code to the repository to determine if it matches, and therepository sends back an authentication if the sent verification codematches the stored verification code. This serves to authenticate a userof the device 104, the device 104 itself, a transaction being performedby the device 104 and other device 106, and/or data sent between devices104, 106 that can be transaction data or other kinds of data. Theverification code can be subdivided and different parts used fordifferent purposes.

The verification code can be separately determined in each device 104,106, and by the fact of entanglement correlation with be the same, yetnot requiring communication of the code outside the devices, thuscreating a shared secret. The shared secret can be used as acryptographic key or onetime pad for the transfer of information such ascredit card numbers, personal user data, or other sensitive informationbetween the authentication terminal and the hand held device. The sharedsecret can be subdivided such that a portion is used for anauthentication code and another portion is used as a cryptographic keyor one-time pad. The verification code can be subdivided and eachsubdivided part used as described herein to perform each of multiplefunctions related to verification, identification and/or secrecy.

FIG. 2A illustrates an embodiment of a time-based state comb 200 for anauthentication and verification system and method using entanglement ofthe present teaching. A time-based state comb 200 is defined by bins 202having a bin length 204, t_(bin), where events are inserted. The bins202 progress along a continuous local time axis 214. A measurement of asingle photon is placed in a time bin, forming an event 206 thatcorresponds to the time along the axis when it was sampled in a bin. Inthe comb 200 of FIG. 2A, there is an event in the first bin 208, thefifth bin 210 and the fourteenth bin 212, of the series of bins that runalong the time axis 214.

In some embodiments, the bins 202 are separated by a bin separation time216. This separation time 216 can be short or long compared to a binlength, t_(bin), 204. The bin separation time 216 may be a period whereno measurement can be made, for example a blanking time in a detector.Thus, the bin separation time 216 can result, for example, fromlimitations of the speed of the detector and/or measurement apparatus.The bin separation time 216 can also just be a period where nomeasurement is chosen to be made. The bin separation time 216 can bechosen to provide a desired time pattern of the comb 200. In someembodiments, the bin separation time 216 is substantially less than,e.g. <<1% of, the bin time 204.

An important feature of the present teaching is the realization thatwhile some embodiments of a comb 200 of the present teaching demandstringent requirements on bin length 204 duration and/or bin separationtime 216 duration, other embodiments are less dependent on theparticular values of bin length 204 and bin separation time 216, as longas these parameters 204, 216 are well defined.

One feature of the present teaching is that cross correlation of combsgenerated through detection of pairs of entangled photons allows thesharing of the entangled quantum states in a way that is robust againstnoise and/or errors in the measurement. In an ideal case, correlatingtwo combs of entangled pairs would yield a count of the number of pairsat the alignment condition and a count of zero at every other position.In practice, noise counts will errantly align, and so positions otherthan pair alignment will have non-zero counts. Combs may be configuredto try to maximize the likelihood that when two combs are aligned, wehave identified the correlated thus alignment of entangled photons. Combprocessing benefits from the statistics of the pair creation versus thenoise. Uncorrelated events that occur at the same time haveprobabilities that multiply. The entangled pair generation is guided bya probability of generation, which is in SPDC systems nominallyproportional to pump energy. The noise photons occur in pairs with aprobability of a single photon squared. This means the noise isnaturally suppressed as compared to the signal of the correlated pairsduring the process of adding the two combs at the alignment position.

FIG. 2B illustrates an embodiment of a time-based state comb 250 for anauthentication and verification system and method using entanglementbeing correlated of the present teaching. A time axis 252 representslocal time at one measurement site that is receiving a stream of singlephotons having one of the pair of generated entangled pairs. In thiscase, the measurement site is the site associated with the comb 254.Similar to the comb described in connection with FIG. 2A, a measurementof a single photon is placed in a time bin, forming an event dot thatcorresponds to the time along the axis when the photon was sampled. Incomb 254 representing measurements of a stream of one of the pair ofentangled photons, there is an event in the first bin, the fifth bin,the tenth bin and the fourteenth bin. The events in the first, fifth andfourteenth bins are actual photon measurements and the tenth bin is anoise measurement.

In a comb 256 representing measurements of a stream of the photons ofthe other of the pair of entangled photons, there is an event in thefirst bin, the third bin and the fourteenth bin. The events in thefirst, fifth and fourteenth bins are actual entangled photonmeasurements and the third bin is a noise measurement. The time bins oftwo combs 254, 256 are slid by each other one-time bin at a time. Thatis, one comb is shifted by a fixed amount relative to the other, and acount of matches is taken at each offset. In some embodiments, theoffset is one bin. At each discrete position, for example the pointwhere time bins of equal size align, a count of the number of correlatedmeasurements, for example, bins aligned that share the same event state,is made. This stepping through offset of combs and compare by adding upmatches at each offset, can be performed using an algorithm. Thealgorithm looks for the position of the set of offset positions with amaximum number of correlated measurements. At a first point in thecorrelation, shown by combs 254, 256, there are no matched states, andthe correlation value is zero.

If a noise event is measured on one comb and not the other, it is notcounted. Because this represents a position where the measurement ofpairs is not aligned, the only matches would be if two noise photonsoverlapped, or a noise event in one comb happened to match a detectedpair photon. The time bins are matched for maximum cross-correlationwhen the count is maximized. This method of matching combs will beunderstood by those skilled in the art as the equivalent of a binarycross correlation function for vectors that consist of just 2 states, 1and zero. For the example shown in FIG. 2B, that occurs where the threeevents line up. The maximum correlation occurs with the position shownin comb 254 and comb 256. The value is three matches. All other offsetpositions had fewer matches. There are no contributions from noisephotons in this example. The number of calculations, or in this case,different relative comb positions that must be added, is equal to thenumber of time bins of a particular measurement comb. This is just anexample, in some embodiments, combs can be thousands, hundreds ofthousands, millions, or billions or more bins long and the process isthe same.

As described herein, time bins 202 of a time-base state comb 200 maycontain a variety of different kinds of state measurement values,including one or more values per photon (bin). For example, bins maycontain markers that indicate simply that a photon was detected(sometimes referred to as an event), or they may include the actualmeasured value of one or more states of that detected photon (e.g.,wavelength or polarization). If a measured value is available, acorrelation is only counted if the measured value matches. This givesthe correlation more specificity, and more noise immunity. This methodwill be understood by those skilled in the art as a variation on a crosscorrelation function, where rather than multiplying values and summing,we are only counting perfect matches. For example, if the states were 1,2, 3, 4, 5 and two states matched with the value of 3, rather thanmultiplying 3×3 then as adding 9 to the total, this method would add 1to the total.

It is possible to provide a closed-form assessment of the noise limitsin some embodiments of the combs of the present teaching. For example,for a case of combs resulting from detections of pairs of entangledphotons, we can define: 1) the P(Entangle Pair Generation)=P(EPG) as theprobability in a single time window an entangled source will give birthto an entangled pair; 2) the P(Noise Detector 1)=P(ND1) as theprobability in a single time window a noise photon will be detected at afirst detector; and 3) the Prob(Noise Detector 2)=Prob(ND2) as theprobability in a single time window a noise photon will be detected at asecond detector.

The cross correlation is represented by a function:

C(k)=Σ_(k=−∞) ^(∞) d1(m)d2(m−k).

For this function, k=offset (that is, the amount the comb is slidforward or backward in time), d1(m) is an array of event values at thefirst detector, and d2(m-k) is an array of offset (by k) event values atthe second detector. The +/−∞ in this case is theoretical. In practicalcases, you can stop calculating C(k) when you have exhausted the eventset. Approaches for practical cross correlation and matching systems andmethods are described in more detail later.

A match is found when a maximum is located for C(k) over all values ofk. When the maximum is found, the combs are correlated when offset by k.The elements that match form a random set that is perfectly correlatedwith another random set.

FIG. 3 illustrates an embodiment of a system 300 for generating a sharedmeasurement comb in time and polarization for an entangled photonauthentication and verification system of the present teaching. Apolarization entangled source 302 produces entangled pairs that emergefrom a pair of ports 304, 306. The first port 304 is illustrated asproducing one of the pair of photons, and the second port 306 isillustrated as producing the other of the pair of photons. In someembodiments, the source 302 generates a photon at the first port 304that is entangled in time and polarization with a photon that emerges atthe second port 302. Thus, when a photon that emerges from the firstport 304 is measured to determine its polarization and time of arrival,those two values will be correlated with the values of a measurement ofpolarization and time of arrival of the paired, entangled, photon thatemerges from the second port 306.

We denote here the two polarization states as H and V as understood bythose skilled in the art as being orthogonal dimensions of polarization.While H is associated with a horizontal dimension and V is associatedwith a vertical dimension, these are arbitrary designations. Values ofpolarization are random variables that emerge from the source ports 304,306. The measured values of the random variables are perfectlycorrelated from pairs. In the case of polarization for many embodiments,measurement of a value H for one photon in a pair produces a value V forthe other measured pair. However, the polarity of the correlation isarbitrary, and depends upon particulars of a measurement configuration.The key is that measured values can be correlated to find a match. Twodifferent polarizations, then can represent a 1 and a 0, and thereforethe set of measured pair values can be represented as a binary number.If only the polarization (or any two-state-dimension basis) is beingused to find a match, it is clear that more than one or even two of themeasured values are needed to establish the match.

It should be understood that a time of arrival of any given photon at adetector is determined by a path length from the source 302 to adetector and that this value of path length may change over time, bothintentionally and non-intentionally. It should also be understood thatit is a time between arrivals of photons from two different sets ofentangled pairs that is the entangled resource. That is, a time betweentwo successive single photon counts at detectors that are measuring twosets of pairs of time-entangled photons will measure the same timebetween events that represent detection of a single photon. The actualtime may be the same as measured against a common clock, but is morelikely to be quite different. It is possible to account for this time offlight difference using an external system that monitors and tracks anyoffset and reports it to the receivers so that it can be accounted for.Alternatively, the receivers themselves can derive time of flightinformation and do local reconciliation.

In some specific embodiments that do not limit the scope of theinvention, the entangled photon source 302 is a crystal pumped by alaser that generates time and polarization entangled photons viaspontaneous parametric down conversion. One of the entangled pairsemerges from port 304, and the other emerges from port 306. The time ofphoton generation is random; however, it is understood that the pairs ofphotons are always generated at precisely the same time. Also, thepolarization of the photons is random. However, the pairs of photonswhen measured, will always be correlated but will have the same or theopposite polarization depending on the specific crystal used and alsothe configuration of the detector. The photons are routed over opticalpaths 308, 310 to two receivers 312, 314. The optical paths 308, 310 canbe free space paths or any kind of guided paths, such as a fiber opticlinks or integrated optical waveguides. It should be understood that thenumerous applications of the methods and apparatus of the presentteaching will require optical paths that are very short for use in, forexample, integrated components and/or mini-free-space optical benchsystems, relatively short for use in, for example, a data or computingcenter, as well as relatively long for use in, for example, applicationsrequiring a long-distance terrestrial, undersea link and/or satellitelink. In other words, depending on the application, the optical paths308, 310 can be on order of microns to on order of many thousands ofkilometers.

The first receiver 312 includes a first single photon detector 316 and asecond single photon detector 318. The detectors 316, 318 have inputsthat are positioned in the optical paths of the outputs of apolarization beam splitter 320. The polarization beam splitter 320 isoriented to pass H-polarized photons to the input of the first detector316 and to pass V-polarized photons to the input of the second detector318. A polarization beam splitter 320 is shown for embodiments where thesecond basis, other than time, is polarization. More generally, anoptical analyzer can be used that directs photons having one state tothe detector 316 and photons with the second state to the seconddetector 318. Thus, the receiver is able to distinguish quantum statesof the basis other than time based on which detector detects theparticular photon. The time basis is measured by the arrival time of theparticular photon at the particular detector 316, 318.

The second receiver 314 includes a first single photon detector 322 anda second single photon detector 324. The detectors 322, 324 have inputsthat are positioned in the optical paths of the outputs of apolarization beam splitter 326. The polarization beam splitter 326 isoriented to pass H-polarized photons to the first detector 322 and topass V-polarized photons to the second detector 324. As with receiver312, this receiver can also be configured to measure other two, andhigher, dimensioned entangled photon but using an analyzer that directsthe photon to a detector 322, 324 based on the value of the state.

The two receivers 312, 314 are also connected via a classical network328. In various embodiments, the classical network 328 can be any of avariety of known networks. For example, the networks can be fiber opticnetworks, wireless networks, satellite networks, free space opticalnetworks and/or combinations of these networks. The network can includeone or more Bluetooth communication channels. A key feature is that itis not necessary that the networks have any particular performancecharacteristics, such as latency guarantees, timing and/orsynchronization requirements, packet loss performance and other knownnetwork performance metrics. Either of the two receivers 312, 314 couldbe part of, for example, the device 104 or the other device 106 of FIG.1 , and the other of the two receivers 312, 314, could be part of theother of the two device 104 or other device 106.

In many embodiments of the system of the present teaching, the receivers312, 314 have information on timing of every, or early every photonarrival. This information can be derived through a combination ofarrivals detected in the detectors 316, 318 or detectors 322, 324 in agiven receiver 312, 314, as well as can the polarization of eacharrival. For example, the detectors can be configured to generate anelectrical signal in response to receiving a single photon in a firststate of polarization at a particular time. This allows the measurementof both the time of arrival and the polarization state. Some or all ofthis information may be included in the comb generated by the processor330, 332 and shared. That is, the processors 330, 332 can process theelectrical signals from each detector, that include informationregarding arrival time of a photon and a polarization state for eachmeasured photon, in a way that uses some or all of the measured stateinformation as needed by a particular comb for a particular application.Combs may include, for example, a list of times of arrival (timing comb)and no polarization state information, and/or a comb may be generated toinclude polarization values and time of arrival. A sequential list ofpolarizations may also be generated using the single photon eventscaptured by the detectors 316, 318, 322, 324.

The system 300 of FIG. 3 can be used for applications that share arandom number that can be used for authentication and verification. Thisshared random number is also secret, in that only the two receivers 312,314 have the shared value. In this application, one of the pair ofphotons arrive at the D1 receiver 312. After passing through or beingreflected by the polarization beam splitter 320, they are detected byeither detector D1H 316 or detector D1V 318 based on their polarization.The time of detection and the polarization are recorded in a timing combgenerated in processor 330 as described herein. One of the pair photonsarrive at the D2 receiver 314. D2's polarization beam splitter 326 isoriented for the same basis as D1's beam splitter 320. When the one ofthe pair of photons strike the polarization beam splitter, they arerouted to either detector D2H 322 or detector D2V 324 based on theirpolarization. The time of detection of and the polarization are recordedin a second timing comb generated in processor 332 as described herein.

Processor 330 in D1 receiver 312 shares its timing comb over a classicalchannel provided by the classical network 328 with just a markindicating windows where a detection occurred and not the polarizationmeasured for the photon that is sampled at the mark. Processor 332 in D2receiver 314 then slides its generated comb in time through the combgenerated by processor 330 and counts the number of correlated detectorhits. By sliding, we mean comparing the two lists at each of a series ofdifferent time shifts between the two lists. By comparing, we meanadding the number of matches per relative time position of the shift. Sotogether by sliding and comparing, we are referring to the ability togenerate a cross-correlation of the two lists. When the number ofcorrelated detector hits is maximized, processor 332 in receiver D2 314uses its measured polarizations in those bins as the correlated datawhich becomes the shared secret.

Although it is not shown in FIG. 3 , either or both of the receivers312, 314 can include quantum storage in front of the analyzer,polarization device 326, that holds the entangled photons for a setperiod of time and can be used to manage the timing of the measurementof the entangled state.

This process of sliding combs to generate a maximum may be referred toherein as a quantum cross-correlation. By sliding the combs in theprocessor 332 to achieve maximum correlation, the time-of-flight fromthe entangled source to each of the receivers is zeroed out andimmaterial to the outcome. It is understood by those skilled in the artthat either receiver 312, 314 can perform the process of sliding combsto determine a maximum. As understood by those skilled in the art, if afixed path length offset is established between the two nodes, then thetime position, or relative offset, determined by the finding of themaximum in the auto-correlation tracks any changes in the relative pathlength. Thus, the combs of the present teaching can be used to determinerelative positions, or relative changes in path length from source 302to receiver 312, 314 in the system 300. The processors 330, 332 use thepolarization values of the matching values found in the correlation as ashared random number.

Referring back to FIG. 1 , a portion of the shared random numbergenerated by the handheld device 104 is used as one side of averification code. A corresponding portion of the shared random numbergenerated by the authentication terminal 106 is used as the other sideof a verification code. A portion of the shared random number is theverification code used by the verification application. When theverification codes are compared and match, a verification process iscomplete, and the handheld device, or an application or data in thehandheld device associated with the verification code, is then verifiedby the verification terminal. The matching process finds the values thatare the random number, and in some embodiments a predeterminedassignment of which portion of the matched values determines the startand stop of the portion of the random number that are verificationcodes.

The particular configuration of the receivers 312, 314 that include apolarizing directing element 320, 326 is just one specific example. Thereceivers may be constructed more generally so long as each detectorgenerates an electrical signal at an output in response to receiving asingle photon in a particular state of an entangled system's possiblestates.

A method for determining quantum entangled state information accordingto the present teaching includes generating a plurality of first photonsand generating a plurality of second photons, wherein the first and thesecond photons have entangled quantum states. The plurality of first andthe plurality of second photons are entangled in at least one basis thatcan include polarization, wavelength, space, and/or time. A firstordered list of events is generated in response to measuring at leastone of a first and second quantum state of at least some of theplurality of first photons. A second ordered list of events is generatedin response to measuring at least one of the first and second quantumstate of at least some of the plurality of second photons. In variousmethods, the first and second ordered list of events can include anordered list of arrival times of single photons, differences betweenarrival times of single photons, an ordered list of polarizationmeasurements, an ordered list of wavelengths, or an ordered list ofspatial position measurements.

The measuring at least one of the first and second quantum state of atleast some of the plurality of first photons can be performed at aphysically different location than the measuring of at least one of thefirst and second quantum state of at least some of the plurality ofsecond photons. The first and second ordered list of events are thencompared to identify entangled quantum state information from theentangled quantum states.

A method for authentication and verification using entangled photonsaccording to the present teaching includes measuring a first pluralityof quantum states and generating a first list comprising values relatedto the measured first plurality of quantum states. A second plurality ofquantum states, where at least some of the second plurality of quantumstates are correlated with at least some of the first plurality ofquantum states is measured. A second list based on the measured secondplurality of quantum states is then generated. The first and secondlists can be lists of, for example, arrival times, differences betweenarrival times, time bins, polarizations, wavelengths, spatial positionsand any combination thereof. The generated first list and generatedsecond list are compared to find related elements. The comparing caninclude a correlation or one of numerous types of pattern matching. Thecomparing can also include sending at least part of one of the first andsecond list over a network. This method can include generatingtimestamps and adding the timestamps to at least one of the first andsecond list. A shared secret is then generated in response to at leasttwo values of the related elements.

A method of determining quantum entanglement according to the presentteaching includes generating an electrical signal in response todetecting a plurality of single photons. The generated electrical signalis then processed to generate a list representing a plurality of arrivaltimes and polarizations of detected single photons. Some of thesemethods also include converting the list representing a plurality ofarrival times and polarizations of detected single photons into a listcomprising time bins. The processing the electrical signal to generatethe list representing the plurality of arrival times and polarization ofdetected single photons comprises determining a time between detectorhits for at least one polarization state and recording the time as anumber. The generated list is then compared with a second list todetermine at least one shared entangled quantum state. The comparisoncan, for example, be a correlation, and/or finding matches or some kindof relationship between the generated list and the second list atdifferent relative positions of elements in the generated list and thesecond list. Once the matches are found, the polarization valuesassociated with each matched item in the generated list and second listare used as a random number. The random numbers in each node derived inthis way are correlated, and known only by the local nodes. As such,these random numbers in each node can form a shared secret randomnumber.

Referring back to FIG. 1 , a portion of the shared secret random numbergenerated by the handheld device 104 is used as one side of averification code. A corresponding portion of the shared secret randomnumber generated by the authentication terminal 106 is used as the otherside of a verification code. A portion of the shared secret randomnumber is the verification code used by the verification application.When the verification codes are compared and match, a verificationprocess is complete, and the handheld device, or an application or datain the handheld device associated with the verification code, is thenverified by the verification terminal. The matching process finds thevalues that are the shared secret random number, and in some embodimentsa predetermined assignment of which portion of the matched valuesdetermines the start and stop of the portion of the random number thatare verification codes.

FIG. 4 illustrates generated combs 400 for an embodiment of anauthentication and verification application using entangled photons ofthe present teaching. The combs 400 are generated with respect to a timeaxis 402, and the alignment shown of the different combs 404, 406, 412in the figure is illustrates a relative position for each comb when theautocorrelation has been maximized. This alignment is more of aconceptual construct as it is determined after the data has beencollected and does not reflect any sort of real-time operation. The timebase 402 is illustrated to represent a common time base for receivers intwo different locations to establish a common sequence of events with,for example, offset times that can be quantified relative this commontime base 402. Alignment with respect to this time base 402 is performedafter the fact of measurement and time base 402 can be arbitrary. Insome embodiments, time-base is a local clock in one or the other nodes.

Referring to both FIGS. 3 and 4 , the comb 404 can be generated by thefirst receiver 312 and the comb 406 can be generated by the secondreceiver 314 and are illustrated with particular measured values ofpolarization 408, 410 (H or V) in each time bin. As can be seen, photonswere measured in bins 1, 5, 10 and 14. Empty time bins have no measuredphotons. A comb 412 is generated to be sent by the classical channel byreceiver D1 312. This comb only exposes the time bins (1, 5, 10 and 14)that measured photons, not the values of polarization. The sharing ofthis comb 412 with receiver 314 and correlation processing in D2receiver 314 with comb 410 reveals the values of the polarization thatrepresent the shared, secret, random number. This is just one example ofhow pattern matching can be used to determine the correlated quantumstates, which can then be used to share a secret that comprises a set ofrandom values.

When available, combs can also contain information from a local clock.In this example, a time comb includes a time stamp from a local clock atthe detector. The indication of what time it is marking is arbitrarilychosen by the user, but in this case, let's say it's pointing at thefirst bin. The time stamp is the setting on the local clock at thedetector when first bin detected that photon. The time stamp is appendedto the comb 412. As described in more detail below, time stamps can beused as follows: 1) to measure the relative distance of two receiversfrom the source because the difference in time stamp values is thedifference in flight time; 2) if the distance is known, a time stamp canbe used to synchronize the clocks at two different receivers; 3) if thelink is initially known to be clear of eavesdroppers, a change in thedifference between time stamps between two receivers can be used toidentify the eves dropper's presence, as the eves dropper adds latency.

Noise can cause detector counts in time bins that are from unwantedsources such as ambient photons and thermal detector noise. Measurementcombs according to the present teaching can help to filter out thesenoise events. FIG. 5 illustrates embodiments of generated combs 500 withnoise in an embodiment of an authentication and verification applicationof the present teaching. Referring to both FIGS. 3 and 5 , a comb 502generated by the first receiver 312 and a comb 504 generated by thesecond receiver 314 are illustrated with particular measured values ofpolarization (H or V) in each time bin. As can be seen, photons weremeasured in bins 1, 3, 5, 8, 10 and 14 in comb 502. Photon were measuredin bins 1, 4, 5, 10, 12 and 14 in comb 504. Empty time bins have nomeasured photons. Noise photons are illustrated in grey and are in bins3, and 8 in comb 502. Noise photons are in bins 4 and 12 in comb 504. Acomb 506 is generated to be sent by the classical channel by receiver D1312. This comb only exposes the time bins (1, 3, 5, 8, 10 and 14) thatindicate measured photons, not the values of polarization. The sharingof this comb 506 with receiver 314 and correlation processing in D2receiver 314 with comb 504 reveals the values of the polarization thatrepresent the shared, secret, random number. The only noise events thatwill result in undetected errors, are noise events that occur in thesame time bin for both D1 and D2. If the probability of a noise event ina given time bin is x, and noise events in the idler and signal pathsare independent, then the probability of a simultaneous noise event isx**2. For example, if noise events occur in 1/1000 of time bins, thenthe undetected error probability is 1/1,000,000.

The combs illustrated in FIGS. 2A-B, 4 and 5 can be referred to as timebin combs that include regularly spaced bins that contain events when ameasurement of that event coincides with the particular bin time, orhappens during a time that falls in a particular bin. It is alsopossible to mark events with timestamps. The scheme for marking eventsdoes not change the basic idea of the combs and comb matching, but itcan have effects on how the matching process is done and/or theresolution of the time aspects of the state values. One feature of theauthentication and verification using entangled photons of the presentteaching is that the shared random numbers can be generated by eitherusing time bin combs or timestamps.

FIG. 6A illustrates state combs 600 with timestamps for an embodiment ofa system and method of authentication and verification usingentanglement of the present teaching. This embodiment relies on eventcombs that comprises events and a measured time between each event. Forexample, an event could be a single photon arrival and the time betweenarrivals can be provided in the comb. As another example, an event caninclude determination of a polarization state of an arrived photon andthe comb presents both a polarization state and a measured time betweenarrivals.

Referring back also to FIG. 3 , receiver 312 detects the single photonsfrom a port 304 of the source 302 and generates electrical signalsrepresenting the time of arrival and polarization of detected photons.The processor 330 converts these electrical signals into a comb 601 thatis illustrated with respect to local measurement time base 602. Thiscomb presents measured polarization states, H or V, 604, 608, and timebetween arrivals 606. In this example, the first polarization state is H604, a time elapses of 0.025 seconds 606, and then a second polarizationstate of V 608 is measured, followed by a time duration of 0.01 secondsto a third detection, in this case a V, and so on. The processordetermines state and the time between detector hits that is recorded anumber. This is in contrast, for example, to the combs 400 described inconnection with FIG. 4 , where detections are connected to a bin number.Comb 601 can be thought of as a continuous-time comb, or a time-stampcomb, as compared, for example to time bin combs 400 illustrated in FIG.4 . The comb 601 can be simply represented as a message, for example,H025V010V135H008 that is sent over the classical network 328 to thesecond receiver 314. Or the comb does not include the polarizationvalues, so that those values remain local, in which case the messagecould be, for example, 025,010,135,008.

A feature of the present teaching is that by comparing local currenttime stamp with the header, it has been determined that offsets intiming between the two receivers 312, 314 can be precisely tracked. Suchinformation could be used for numerous applications and systems can beconfigured to achieve difficult or even otherwise impossible tasks. Forexample, if differences in optical path delays between receivers 312,214 and source 302 are known or separately tracked, sharing the comb 601with timestamps can maintain extremely precise or even near oressentially perfect synchronization of the local clocks in the receivers312, 314. Since for example, SPDC systems generate entangled photons atexactly the same instance in time, wherein the synchronization accuracyof such a system is only limited by the precision of the detectors. Insome systems, the precision will essentially depend only the accurate ofthe relative positions, which can be determined with a high level ofprecision with interferometric techniques. In some particular methodsaccording to the present teaching, regardless of the known offset intransit time, the second receiver 314 adjusts the local clock by findingthe difference between the timestamps, taking account of time-of-flightoffset, and adjusting the local clock based on the remaining differencethat represents a synchronization error.

As another example, if precise free running clocks are available in thereceivers 312, 314, sharing the comb 601 with timestamps can be used todetermine optical path differences between the nodes 312, 314 and/orsource 302. The differences can be intentional differences that might bepart of a signaling scheme. The difference can be unintentionaldifferences, that might be used to correct or control other timing-basedprocessing that is ongoing within and amongst the receivers 312, 314.The local clock adjustment and/or optical path difference determinationscan be included as part of the authentication and verification system.In some embodiments, some of the measured state values are applied tothe adjusting and/or path difference determinations and others of themeasured state values are applied to the verification code.

FIG. 6B illustrates the embodiment of state combs 630 for the system andmethod of authentication and verification using entanglement with noiseof the present teaching. The event measurements along time axis 632include a pair photon H 636, then a noise, or errant, measurement V 6340.025 seconds later, then a pair photon V 640 0.10 seconds later, and soon. The other pair measurement system receives in comb 642 a pair H 644,then a pair photon V 646 0.035 seconds later, and so on. The first paircomb may be represented H025V010V135H008V. The second pair comb may berepresented H035V135H008V.

It is possible to correlate these combs in various ways. For example,FIG. 6C illustrates an embodiment of correlating state combs of FIG. 6B.The combs 634, 642 may be converted into tiny time bins where the sizeof the bin is related to the accuracy of the clock measuring inter-tickarrivals. Thus comb 634 is represented as time diagram 652. Comb 642 isrepresented as time diagram 654. Then, the correlation is equivalent tothe time bin method, with likely small (narrower window) time bins. Thematched position in the example time diagrams 652, 6 FIG. 6C illustratesan embodiment of correlating state combs of FIG. 6B 54 yields acorrelated value of four. In this case, only a few alignments with thesingle noise photon have a summed value of one.

Other matching methods can also be applied. The birth times of entangledphotons are absolutely simultaneous, thus T1, T2, . . . Ti are veryprecisely defined. If an exact time interval match is found whencomparing combs, and the local clock is very precise (ticks are short induration), then it is likely that a single match of inter-photon arrivaltimes defines the entire ensemble. If the first position doesn't work, asecond random position or a third will likely yield a match. As theaccuracy of your clock improves, the probability of a match of theensemble, given a match of a single interval, improves as well. Ingeneral, it is possible to step through time values added to all eventsin one comb and compare the two combs at each of these values, most ofwhich will not yield many matches until a value is found that has alarge number of matching time stamps.

Numerous data processing algorithms can be used to process measured datato compensate for noise. Noise can be defined for some applications asthe probability of an erroneous non-entangled photon detection. Whendetermining a match based on a single interval, it is important todefine the measurement interval for the appropriate level of noise. Forexample, if a noise photon (such as the errant V measurement describedin connection with FIG. 6B) is measured between the reception of twoentangled photons, it should be ignored when processing the data. Whentime matching, the algorithm employed can, for example, add togetheradjacent intervals when single interval matches are not seen (forexample, the T1+T2 described in connection with FIG. 6C).

One feature of the present teaching is that the combs can be processedusing a variety of methods to find matches between combs. As describedherein, for example, a cross-correlation of time-binned data produces apeak at a match position, and the elements of either comb that occupythat match position are nominally all correlated states. The regulartime bins provide a basis for the time comparison between the data inthe two combs. For example, time bins provide the basis for k in theequation C(k) described earlier.

One feature of the present teaching is that certain information abouttiming at different nodes and/or different detectors that are sharingcombs can be used to improve the efficiency of the matching processand/or algorithm. For example, having knowledge of an absolute time atD1 and D2 (that is, detector(s), D1 that receive one of a pair ofentangled photons and D2 that receive the other one of the pair) canreduce the range over which two vectors need to look for a match.Various known methods and systems can be used to provide this absolutetime information. For example, GPS can provide accurate absolute time atmultiple locations with an accuracy on the order of forty nanoseconds.Various classical network clock synchronization schemes, for example,Building Integrated Timing Supply (BITS), where timing information issent along a standard telecommunication connection, can also be used toobtain absolute time. Using an internet connection, for example, NetworkTime Protocol (NTP) is generally accurate to about 0.01 seconds. Othercustomized options can also be used. For example, a one nanosecondaccuracy scheme known as White Rabbit is used in some time-sensitivephysics infrastructure. A physical “wire” or other connection with knownor trackable latency between D1 and D2 can be used. A common clock canbe used at D1 and D2.

For separated nodes, having some knowledge about the relative time offlight to D1 and D2 from the pair-generation point can be useful. If thelocations are fixed, location offset can be normalized out to zero. Ifthe locations are moving, a location offset can be set to maximummovement allowed in the system. For example, a ranging system (RADAR)that detects within 20 miles, would have a maximum ten millisecondoffset. It is possible to use delta encoding for this time of flight.For example, if an object is moving, it doesn't displace from locationX1 to location X2 instantly, it has a velocity, so time betweenmeasurements can be accordingly constrained by velocity of the object.

In some embodiments, timestamps can be converted into time-binnedvectors and then cross-correlated to find the match offset. In someembodiments, the binned timestamps result in a very large and/or verysparse vector if the stamp time resolution is very high. As such, insome embodiments, steps are taken to reduce the number of bits in thetime stamp. For example, a 64-bit time stamp, at 125-ps resolution, has8 billion ticks per second. Sixty-four bits can count to 18{circumflexover ( )}19 units, equivalent to seventy-four years. Thirty-two bits cancount to 4 billion ticks, so looking at a second of timestamp datarequires about thirty-three bits, while looking at 10 seconds of datarequires about thirty-seven bits. As such, the timestamp needs lessprecision based on the knowledge about clocks and time-of-flight betweendetectors sharing combs.

In some embodiments, the precision of the timestamp is chosen to reducea processing time (e.g. comb vector length) while maintaining asufficient time resolution to find entangled correlations within a givenbackground singles level. For example, for an entanglement generationrate of about ten pairs per second, a timestamp resolution of 125picoseconds allows detection of entangled pairs with a low (<1%) errorrate in a background of between 50K-100K counts per second. A timestampresolution of one nanosecond allows detection of entangled pairs with alow (<1%) error rate in a background of between 5K-20K counts persecond. A timestamp resolution of sixteen nanoseconds allows detectionof entangled pairs with a low (<1%) error rate in a background ofbetween 1K-4K counts per second. So, moving from 125 picosecondresolution timestamps to 1 ns resolution timestamps can take one to twooff the above precision requirements. These optimizations can serve toreduce implementation costs depending on specific system requirements.

One feature of the present teaching is that algorithmic methods can beused for finding matches. Rather than translating time stamps into largesparse vectors of 0 and 1's (time-binning), it is possible to workdirectly with the time stamps. Various known methods can be used. Forexample, the simple brute force comparison search method can be used tolook for matches. Additionally, a divide and conquer method that uses aprogressive search, starting in the middle of the data series beingcompared and working by dividing by two each time can be used. Thisapproach can reduce searches to on the order of n steps rather than anorder of 2{circumflex over ( )}n steps.

One feature of the specialized hardware can be used to improve the speedand efficiency of methods and systems of finding matches. For example,some embodiments, rather than a traditional Turing-machine search,utilize Content Addressable Memory (CAM) can be used. Some embodimentsutilize specialized hardware that increments all stamps in a comb by onetick all at once and compares a large number of stamps to count matchesin one cycle can be used. Some embodiments utilize state machines thatare built using application specific circuits (ASICs). Some embodimentsrely on known graphics and AI chips that include multiple processors todo functions that are equivalent to the batch increment and matching.For example, NVIDIA chips can be used that take advantage of the naturalparallelism of the add and compare aspects of the computation.

One feature of the authentication and verification method and system ofpresent teaching is that it can be extended to include a trustedauthority. FIG. 7 illustrates an embodiment of an authentication andverification system and method using entangled photons with a trustedauthority of the present teaching. A trusted authority 702 includes asecure repository 704. An entangled source 706 produces pairs ofphotons, with one of the pair transported to a device 708 and the otherof the pair transported to another device 710. These devices 708, 710are similar to the devices 104, 106 described in connection with FIG. 1. The device 708 can be a handheld device or other personal device. Andthe other device 710 can be an authentication terminal or other point ofsale device. The devices 708, 710 are connected by a classical channel712 that could be a Bluetooth channel. The secure repository 704 isconnected to a classical network 714 that connects remote locations. Aremote authenticator 716 includes an entangled source 718. The entangledsource 718 produces pairs of photons, with one of the pair transportedto a device 708 and the other of the pair transported to another device720. The device 708 and the other device 720 are connected by aclassical channel 722 that could be a Bluetooth channel. The otherdevice 720 in the remote authenticator 716 is connected to the classicalnetwork 714. The device 708 is connected to the classical network 714.

The authentication with trusted authority system 700 can work inmultiple different ways, two of which will be described further. First,the party being authenticated can be assured that the authenticationauthority is the legitimate from a cold start as follows. A user with adevice 708 goes to the trusted authority 702. The trusted authority 702could reside in a bank or an ATM or other location. The trustedauthority 702 identifies the user by some means. For example, they knowthe user, user biometrics, license, passport, bank account numbers,mother's maiden name or other means. The trusted authority 702 shares arandom number via quantum means as discussed herein by connecting to thesource 706. The random number is shared by the device 708 and the otherdevice 710 and a portion of this random number is a verification codethat is shared. The device 710 puts the code in a secure repository 704with the identification information of the user. Only the user's device708 and the authority's repository 704 know the verification code. Insome embodiments, even the personnel at the trusted authority don't needto know the verification code. When the user wants to be identified,they go to a remote authenticator 716 and get a verification code thatis created there by them connecting their device 708 (which for this usecase is the same device 708 used in the trusted authority 702). In someembodiments the verification code, or part of the verification code, isused as a crypto key to encrypt information transfer at the remoteauthenticator 716. The user's device 708 then sends N-bits of the sharedsecret random number from the verification code generated on the earlierencounter with the trusted authority 702 over the classical network 714.This shared secret random number from the verification code is sent overthe classic network 714, because it has no meaning to any observer thantrusted authority 702. The trusted authority looks for a match withshared secret random number from the verification code in the securerepository 704. If there is a match, it must be the user, and a YES issent to the device 720 at the remote authenticator 716. This, then,serves to authenticate the user in the system 700. As indicated herein,a user can be, for example, an individual, a sensor, a computing device,a robot, a machine, a drone and numerous other persons or devices thathave an identity and/or a role in a system.

In some embodiments, the trusted authority 702 now sends to the user thenext N-bits of the shared secret shared secret random number from theverification code via the classical network 714. Note that only trustedauthority 702 and end user device 708 knows these bits. So, when theuser receives the bits they know it must be from the trusted authoritywith which the initial encounter occurred.

In some embodiments, it is possible that in the remote authenticator 716classical exchanges between the device 708 and other device 720 alsoperform additional sharing of combs to find error free bits. In someembodiments, it can be even more secure to send the noise bits too, anddo the cross-correlation, or matching process, post-facto, at theauthentication event in the remote authenticator 716. This way thetransaction looks even more non-sensical, like noise, to an observer.The voracity of the trusted authority 702 depends on the handheld device708 data and repository data 708 being kept secure by the user andtrusted authority 702.

Referring to both FIGS. 1 and 7 , in some embodiments, the device 106,720 is a point-of-sale terminal. In some embodiments, the verificationcode is used to mark a purchase. In some embodiments, the verificationcode is used as a crypto key and verification of a credit card number ina point of sale transaction. In some embodiments, the verification codeis used to provide access, and the authentication terminal 106, 720 isused to grant access. These are just examples of uses for theverification method using entangled photons of the present teaching.

EQUIVALENTS

While the Applicant's teaching is described in conjunction with variousembodiments, it is not intended that the applicant's teaching be limitedto such embodiments. On the contrary, the Applicant's teachingencompasses various alternatives, modifications, and equivalents, aswill be appreciated by those of skill in the art, which may be madetherein without departing from the spirit and scope of the teaching.

1-20. (canceled)
 21. A method of generating a verification code, themethod comprising: a) measuring a time of arrival and a correspondingfirst or second state value of a plurality of first photons, whereinrespective ones of the plurality of first photons are entangled withrespective ones of a plurality of second photons in a first basis, whichis time, and entangled in a second basis; b) generating a first orderedlist of the measured times of arrival of the plurality of first photons;c) measuring a time of arrival and a corresponding first or second statevalue of the plurality of second photons; d) generating a second orderedlist of the measured times of arrival of the plurality of secondphotons; e) determining time-of-arrival matches between the firstordered list and the second ordered list; f) determining first or secondstate values that correspond to the determined time-of-arrival matchesbetween the first ordered list and the second ordered list; and g)generating a verification code using at least some of the determinedfirst or second state values that correspond to the determinedtime-of-arrival matches.
 22. The method of claim 21 further comprisingsending the generated verification code to a trusted authority.
 23. Themethod of claim 22 further comprising querying the trusted authority.24. The method of claim 23 further comprising using a result of thequery to make a conclusion on authenticating.
 25. The method of claim 23further comprising using the result of the query to authenticate adevice.
 26. The method of claim 21 further comprising attaching theverification code to data.
 27. The method of claim 21 further comprisingusing the verification code as a unique identifier.
 28. The method ofclaim 21 further comprising performing a cryptographic operation withthe verification code.
 29. The method of claim 28 further comprisingusing the verification code as a cryptographic key.
 30. The method ofclaim 21 wherein the plurality of first photons and the plurality ofsecond photons are further entangled in a third basis.
 31. The method ofclaim 30 further comprising measuring both a time of arrival and acorresponding state value of the third basis of the plurality of firstphotons and the plurality of second photons, and then determining errorsin the verification code from the measured corresponding state values ofthe third basis.
 32. The method of claim 30 further comprising measuringboth a time of arrival and a corresponding state value of the thirdbasis of the plurality of first photons and the plurality of secondphotons, and then producing additional bits in the verification codefrom the measured corresponding state values of the third basis.
 33. Themethod of claim 21 further comprising subdividing the verification codeinto a plurality of verification codes.
 34. The method of claim 21further comprising: a) measuring a time of arrival and a correspondingfirst or second state value of a plurality of third photons, whereinrespective ones of the plurality of third photons are entangled withrespective ones of a plurality of fourth photons in a first basis, whichis time, and entangled in a second basis; b) generating a third orderedlist of the measured time of arrival of the plurality of third photons;c) measuring a time of arrival and a corresponding first or second statevalue of a plurality of fourth photons; d) generating a fourth orderedlist of the measured time of arrival of the plurality of fourth photons;e) determining time-of-arrival matches between the third ordered listand the fourth ordered list; f) determining first or second state valuesthat correspond to the determined time-of-arrival matches between thethird and fourth ordered lists; and g) generating a second verificationcode with at least some of the determined first and second state valuesthat correspond to the time-of-arrival matches of the third and fourthordered lists.
 35. The method of claim 34 further comprising sending thegenerated second verification code to a trusted authority.
 36. Themethod of claim 35 further comprising querying the trusted authority andusing a result of the query to make a conclusion on authenticating. 37.The method of claim 34 further comprising attaching the secondverification code to data.
 38. The method of claim 34 further comprisingusing the second verification code as a unique identifier.
 39. Themethod of claim 34 further comprising performing a first cryptographicoperation with the verification code and a second cryptographicoperation with the second verification code.
 40. The method of claim 39further comprising using a result of both the first and the secondcryptographic operation as a cryptographic key.
 41. The method of claim34 wherein the plurality of third photons and the plurality of fourthphotons are further entangled in a third basis.
 42. The method of claim41 further comprising measuring both a time of arrival and acorresponding state value of the third basis of the plurality of thirdphotons and the plurality of fourth photons, and then determining errorsin the second verification code from the measured corresponding statevalues of the third basis.
 43. The method of claim 41 further comprisingmeasuring both a time of arrival and a corresponding state value of thethird basis of the plurality of third photons and the plurality offourth photons, and then producing additional bits in the verificationcode from the measured corresponding state values of the third basis.44. The method of claim 34 further comprising subdividing the secondverification code into a plurality of second verification codes.
 45. Areceiver for verification, the receiver comprising: a) a first devicehaving input that receives a plurality of first photons and that isconfigured to measure both a time of arrival and a corresponding firstor second state value of the plurality of first photons, and configuredto generate at an output an ordered list of the measured times ofarrival of the plurality of first photons; b) a second device havinginput that receives a plurality of second photons, wherein respectiveones of the plurality of first photons are entangled with respectiveones of the plurality of second photons in a first basis, which is time,and entangled in a second basis, the second device being configured tomeasure both a time of arrival and a corresponding first or second statevalue of the plurality of second photons, and configured to generate atan output an ordered list of the measured times of arrival of theplurality of second photons; and c) a processor connected to the outputof the first device and the output of the second device and configuredto receive the ordered list of the measured times of arrival of theplurality of first photons and the ordered list of the measured times ofarrival of the plurality of second photons, the processor furtherconfigured to determine time-of-arrival matches between the ordered listof the measured times of arrival of the plurality of first photons andthe ordered list of the measured times of arrival of the plurality ofsecond photons, further configured to determine first or second statevalues that correspond to the time-of-arrival matches, and furtherconfigured to generate a verification code with at least some of thedetermined first or second state values that correspond to thetime-of-arrival matches.
 46. The receiver of claim 45 wherein theprocessor is further configured to send the generated verification codeto a trusted authority, to query the trusted authority, and to use aresult of the query to authenticate.
 47. The receiver of claim 45wherein the processor is further configured to attach the verificationcode to data.
 48. The receiver of claim 45 wherein the processor isfurther configured to perform a cryptographic operation with theverification code.
 49. The receiver of claim 45 further comprising athird device having an input that receives a plurality of third photonsand an output that is connected to the processor.
 50. A method ofgenerating a verification code, the method comprising: a) measuring atime of arrival and a corresponding first or second state value of aplurality of first photons and a plurality of second photons, whererespective ones of the plurality of first photons are entangled withrespective ones of a plurality of second photons in a first basis, whichis time, and entangled in a second basis; b) generating a first and asecond ordered list of the measured times of arrival of the plurality ofrespective first and second photons; c) determining time-of-arrivalmatches between the first ordered list and the second ordered list; d)determining first or second state values that correspond to thedetermined time-of-arrival matches between the first ordered list andthe second ordered list; and e) generating a verification code usingsome of the determined first or second state values that correspond tothe determined time-of-arrival matches.